Economical (k,m)-threshold controlled quantum teleportation

We study a (k,m)-threshold controlling scheme for controlled quantum teleportation. A standard polynomial coding over GF(p) with prime p>m-1 needs to distribute a d-dimensional qudit with d >= p to each controller for this purpose. We propose a scheme using m qubits (two-dimensional qudits) for the controllers' portion, following a discussion on the benefit of a quantum control in comparison to a classical control of a quantum teleportation.